DOI: 10.1126/science.1133687, 1118 (2006);314 Science

et al.Josh BongardResilient Machines Through Continuous Self-Modeling

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success in recovering both previously unknowncave bear and known Neanderthal genomicsequences using direct genomic selection indicatesthat this is a feasible strategy for purifying specificcloned Neanderthal sequences out of a highbackground of Neanderthal and contaminatingmicrobial DNA. This raises the possibility that,should multiple Neanderthal metagenomic libra-ries be constructed from independent samples,direct selection could be used to recover Neander-thal sequences from several individuals to obtainand confirm important human-specific and Nean-derthal-specific substitutions.

Conclusions. The current state of our knowl-edge concerning Neanderthals and their relationshiptomodernhumans is largely inferenceandspeculationbased on archaeological data and a limited number ofhominid remains. In this study,we have demonstratedthatNeanderthal genomic sequences canbe recoveredusing ametagenomic library-based approach and thatspecific Neanderthal sequences can be obtained fromsuch libraries by direct selection. Our study thus pro-vides a framework for the rapid recovery of Nean-derthal sequences of interest from multipleindependent specimens, without the need for whole-genome resequencing. Such a collection of targetedNeanderthal sequences would be of immense valuefor understanding human and Neanderthal biology

and evolution. Future Neanderthal genomic studies,including targeted and whole-genome shotgunsequencing, will provide insight into the profoundphenotypic divergence of humans both from the greatapes and from our extinct hominid relatives, and willallowus to explore aspects ofNeanderthal biologynotevident from artifacts and fossils.

References and Notes1. P. Mellars, Nature 432, 461 (2004).2. F. H. Smith, E. Trinkaus, P. B. Pettitt, I. Karavanic, M. Paunovic,

Proc. Natl. Acad. Sci. U.S.A. 96, 12281 (1999).3. M. Krings et al., Cell 90, 19 (1997).4. M. Krings et al., Proc. Natl. Acad. Sci. U.S.A. 96, 5581

(1999).5. S. Pääbo et al., Annu. Rev. Genet. 38, 645 (2004).6. D. Serre et al., PLoS Biol. 2, e57 (2004).7. M. Currat, L. Excoffier, PLoS Biol. 2, e421 (2004).8. S. G. Tringe et al., Science 308, 554 (2005).9. S. G. Tringe, E. M. Rubin, Nat. Rev. Genet. 6, 805 (2005).10. J. P. Noonan et al., Science 309, 597 (2005).11. M. Margulies et al., Nature 437, 376 (2005).12. H. N. Poinar et al., Science 311, 392 (2006).13. Materials and methods are available as supporting

material on Science Online.14. S. F. Altschul et al., Nucleic Acids Res. 25, 3389 (1997).15. Chimpanzee Sequencing and Analysis Consortium, Nature

437, 69 (2005).16. M. Hofreiter et al., Nucleic Acids Res. 29, 4793 (2001).17. S. Kumar, A. Filipski, V. Swarna, A. Walker, S. B. Hedges,

Proc. Natl. Acad. Sci. U.S.A. 102, 18842 (2005).18. N. Patterson, D. Richter, S. Gnerre, E. Lander, D. Reich,

Nature, in press; published online 17 May 2006(10.1038/nature04789).

19. The International HapMap Consortium et al., Nature437, 1299 (2005).

20. B. F. Voight et al., Proc. Natl. Acad. Sci. U.S.A. 102,18508 (2005).

21. A. M. Adams, R. R. Hudson, Genetics 168, 1699 (2004).22. I. McDougall et al., Nature 433, 733 (2005).23. V. Plagnol, J. D. Wall, PLoS Genet., in press (110.1371/

journal.pgen.0020105.eor).24. S. Bashiardes et al., Nat. Methods 2, 63 (2005).25. P. Mellars, Nature 439, 931 (2006).26. Neanderthal sequences reported in this study have been

deposited in GenBank under accession numbers DX935178to DX936503.We thank E. Green, M. Lovett, andmembers ofthe Rubin, Pääbo, and Pritchard laboratories for insightfuldiscussions and support. J.P.N. was supported by NIHNational Research Service Award fellowship 1-F32-GM074367. G.C. and S.K. were supported by grant R01HG002772-1 (NIH) to J.K.P. This work was supported bygrant HL066681, NIH Programs for Genomic Applications,funded by the National Heart, Lung and Blood Institute; andby the Director, Office of Science, Office of Basic EnergySciences, of the U.S. Department of Energy under contractnumber DE-AC02-05CH11231.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/314/5802/1113/DC1Materials and MethodsFigs. S1 to S6Tables S1 to S12References

16 June 2006; accepted 17 August 200610.1126/science.1131412

REPORTS

Resilient Machines ThroughContinuous Self-ModelingJosh Bongard,1*† Victor Zykov,1 Hod Lipson1,2

Animals sustain the ability to operate after injury by creating qualitatively different compensatorybehaviors. Although such robustness would be desirable in engineered systems, most machines failin the face of unexpected damage. We describe a robot that can recover from such changeautonomously, through continuous self-modeling. A four-legged machine uses actuation-sensationrelationships to indirectly infer its own structure, and it then uses this self-model to generateforward locomotion. When a leg part is removed, it adapts the self-models, leading to thegeneration of alternative gaits. This concept may help develop more robust machines and shedlight on self-modeling in animals.

Robotic systems are of growing interestbecause of their many practical applica-tions as well as their ability to help

understand human and animal behavior (1–3),cognition (4–6), and physical performance (7).Although industrial robots have long been used

for repetitive tasks in structured environments,one of the long-standing challenges is achievingrobust performance under uncertainty (8). Mostrobotic systems use a manually constructedmathematical model that captures the robot’sdynamics and is then used to plan actions (9).Although some parametric identification methodsexist for automatically improving these models(10–12), making accurate models is difficult forcomplex machines, especially when trying toaccount for possible topological changes to thebody, such as changes resulting from damage.

Fig. 7. Recovery of Neanderthal genomic sequences from library NE1 by direct genomic selection.

1Mechanical and Aerospace Engineering, Cornell Univer-sity, Ithaca, NY 14853, USA. 2Computing and InformationScience, Cornell University, Ithaca, NY 14853, USA.

*Present address: Department of Computer Science,University of Vermont, Burlington, VT 05405, USA.†To whom correspondence should be addressed. E-mail:josh.bongard@uvm.edu

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Although much progress has been made inallowing robotic systems to model their environ-ment autonomously (8), relatively little is knownabout how a robot can learn its own morphology,which cannot be inferred by direct observation orretrieved from a database of past experiences (13).Without internalmodels, robotic systems can auton-omously synthesize increasingly complex behaviors(6, 14–16) or recover from damage (17) throughphysical trial and error, but this requires hundreds orthousands of tests on the physical machine and isgenerally too slow, energetically costly, or risky.

Here, we describe an active process that allowsa machine to sustain performance through anautonomous and continuous process of self-modeling. A robot is able to indirectly infer itsownmorphology through self-directed explorationand then use the resulting self-models to synthesizenew behaviors. If the robot’s topology unexpect-edly changes, the same process restructures itsinternal self-models, leading to the generation ofqualitatively different, compensatory behavior. Inessence, the process enables the robot to continu-ously diagnose and recover from damage. Unlikeother approaches to damage recovery, the conceptintroduced here does not presuppose built-inredundancy (18, 19), dedicated sensor arrays, orcontingency plans designed for anticipated failures(20). Instead, our approach is based on the conceptof multiple competing internal models and gener-ation of actions to maximize disagreementbetween predictions of these models.

The process is composed of three algorithmiccomponents that are executed continuously by thephysical robot while moving or at rest (Fig. 1):Modeling, testing, and prediction. Initially, therobot performs an arbitrary motor action andrecords the resulting sensory data (Fig. 1A). Themodel synthesis component (Fig. 1B) then syn-thesizes a set of 15 candidate self-models usingstochastic optimization to explain the observedsensory-actuation causal relationship. The actionsynthesis component (Fig. 1C) then uses thesemodels to find a new actionmost likely to elicit themost information from the robot. This isaccomplished by searching for the actuation patternthat, when executed on each of the candidate self-models, causes the most disagreement across thepredicted sensor signals (21–24). This new actionis performed by the physical robot (Fig. 1A), andthemodel synthesis component now reiterates withmore available information for assessing modelquality. After 16 cycles of this process haveterminated, the most accurate model is used bythe behavior synthesis component to create adesired behavior (Fig. 1D) that can then beexecuted by the robot (Fig. 1E). If the robot detectsunexpected sensor-motor patterns or an externalsignal as a result of unanticipated morphologicalchange, the robot reinitiates the alternating cycle ofmodeling and exploratory actions to produce newmodels reflecting the change. The new mostaccurate model is now used to generate a new,compensating behavior to recover functionality. Acomplete sample experiment is shown in Fig. 2.

We tested the proposed process on a four-legged physical robot that had eight motorizedjoints, eight joint angle sensors, and two tilt sensors.The space of possiblemodels comprised any planartopological arrangement of eight limbs, includingchains and trees (for examples, see Figs. 1 and 2).After damage occurs, the space of topologies isfixed to the previously inferredmorphology, but thesize of the limbs can be scaled (Fig. 2, N and O).The space of possible actions comprised desiredangles that the motors were commanded to reach(25). Many other self-model representations couldreplace the explicit simulations used here, such asartificial neural or Bayesian networks, and othersensory modalities could be exploited, such aspressure and acceleration (here the joint anglesensors were used only to verify achievement ofdesired angles, and orientation of the main bodywas used only for self-model synthesis). None-theless, the use of implicit representations such asartificial neural networks—although more biologi-cally plausible than explicit simulation—wouldmake the validation of our theorymore challenging,

because it would be difficult to assess thecorrectness of the model (which can be done byvisual inspection for explicit simulations). Moreimportant, without an explicit representation, it isdifficult to reward a model for a task such asforward locomotion (which requires predictionsabout forward displacement) when the model canonly predict orientation data.

The proposed process was compared with twobaseline algorithms, both of which use randomrather than self-model–driven data acquisition. Allthree algorithm variants used a similar amount ofcomputational effort (~250,000 internal modelsimulations) and the same number (16) of physicalactions (Table 1). In the first baseline algorithm, 16randomactionswere executed by the physical robot(Fig. 1A), and the resulting data were supplied tothe model synthesis component for batch training(Fig. 1B). In the second baseline algorithm, theaction synthesis component output a randomaction,rather than searching for one that created dis-agreement among competing candidate self-models. The actions associated with Fig. 1, A to C,

Fig. 1. Outline of the algorithm. The robot continuously cycles through action execution. (A and B)Self-model synthesis. The robot physically performs an action (A). Initially, this action is random;later, it is the best action found in (C). The robot then generates several self-models to matchsensor data collected while performing previous actions (B). It does not know which model iscorrect. (C) Exploratory action synthesis. The robot generates several possible actions thatdisambiguate competing self-models. (D) Target behavior synthesis. After several cycles of (A) to(C), the currently best model is used to generate locomotion sequences through optimization. (E)The best locomotion sequence is executed by the physical device. (F) The cycle continues at step (B)to further refine models or at step (D) to create new behaviors.

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were cycled as in the proposed algorithm, butFig. 1C output a random action, rather than anoptimized one.

Thirty experiments of each of the three al-gorithm variants were conducted, both before andafter the robot suffered damage. Before damage,the robot began each experiment with a set ofrandommodels; after damage, the robot beganwiththe best model produced by the model-drivenalgorithm (Fig. 2F). We found that the probabilityof inferring a topologically correct model wasnotably higher for the model-driven algorithm thanfor either random baseline algorithm (Table 1) andthat the final models were more accurate onaverage in the model-driven algorithm than ineither random baseline algorithm (Table 1). Sim-ilarly, after damage, the robot was better able toinfer that one leg had been reduced in length usingthe model-driven algorithm than it could usingeither baseline algorithm (Table 1). This indicatesthat alternating random actions with modeling,compared with simply performing several actionsfirst and then modeling, does not improve modelsynthesis (baseline 2 does not outperform base-line 1), but a robot that actively chooses whichaction to perform next on the basis of its current setof hypothesized self-models has a better chance ofsuccessfully inferring its own morphology than arobot that acts randomly (the model-driven algo-rithm outperforms baseline algorithms 1 and 2).

Because the robot is assumed not to know itsown morphology a priori, there is no way for it todetermine whether its current models have capturedits body structure correctly. We found that dis-agreement among the currentmodel set (informationthat is available to the algorithm) is a good indicatorof model error (the actual inaccuracy of the model,which is not available to the algorithm), because apositive correlation exists between model dis-agreement and model error across the n = 30experiments that use the model-driven algorithm(Spearman rank correlation = 0.425, P < 0.02).Therefore, the experiment that resulted in the mostmodel agreement (through convergence toward thecorrect model) was determined to be the mostsuccessful from among the 30 experiments per-formed, and the best model it produced (Fig. 2F)was selected for behavior generation. This was alsothe starting model that the robot used when itsuffered unexpected damage (Table 1).

The behavior synthesis component (Fig. 1D)was executed 30 times with this model, startingeach time with a different set of random behaviors.Figure 3 reports the final positions predicted by themodel robot using the best behavior produced byeach experiment (black dots). Each of those 30behaviors was then executed on the physical robot,and the resulting actual positions are reported inFig. 3 (blue dots). As a control, 30 random be-haviors were also executed on the physical robot(red dots). Although there is some discrepancy be-tween the predicted distance and actual distance,there is a clear forward motion trend that is absentfrom the random behaviors. This indicates that thisautomatically generated self-model was sufficiently

predictive to allow the robot to consistently developforward motion patterns without further physicaltrials. One of the better locomotion patterns isshown in fig. S1A. The transferal from the self-model to reality was not perfect, although the gaitswere qualitatively similar; differences between thesimulated and physical gait (seen at 2.6 and 5.2 s)were most likely due to friction and kinematicbifurcations at symmetrical postures, both difficultto predict. Similarly, after damage, the robot wasable to synthesize sufficiently accurate models (anexample is given in Fig. 2O) for generating new,compensating behaviors that enabled it to continuemoving forward. An example of a compensatinggait is shown in fig. S1B and movie S1.

Although the possibility of autonomous self-modeling has been suggested (26), we demonstratedfor the first time a physical system able toautonomously recover its own topology with littleprior knowledge, as well as optimize the parametersof those resulting self-models after unexpected

morphological change. These processes demon-strate both topological andparametric self-modeling.This suggests that future machines may be able tocontinually detect changes in their ownmorphology(e.g., after damage has occurred or when grasping anew tool) or the environment (when the robot entersan unknown or changed environment) and use theinferred models to generate compensatory behavior.Beyond robotics, the ability to actively generate andtest hypotheses can lead to general nonlinear andtopological system identification (23) in otherdomains, such as computational systems (22),biological networks (23), damaged structures (24),and even automated science (27).

This work may inform future investigations ofcognition in animals and the development ofcognition in machines. Whereas simple yet robustbehaviors can be created for robots withoutrecourse to a model (14–17, 28), higher animalsrequire predictive forward models to function,given that in many cases biological sensors are

Fig. 2. The robot contin-uallymodels and behaves.The robot performs a ran-dom action (A). A set ofrandom models, such as(B), is synthesized into ap-proximatemodels, such as(C). A new action is thensynthesized to createmax-imal model disagreementand is performed by thephysical robot (D), afterwhich further modelingensues. This cycle contin-ues for a fixed period oruntil no further modelimprovement is possible(E and F). The best modelis then used to synthesizea behavior. In this case,the behavior is forwardlocomotion, the first fewmovements of which areshown (G to I). This be-havior is then executed bythe physical robot (J to L).Next, the robot suffersdamage [the lower partof the right leg breaks off(M)]. Modeling recom-mences with the bestmodel so far (N), andusing the same processof modeling and experi-mentation, eventually dis-covers the damage (O).The new model is used tosynthesize a new behav-ior (P to R), which is ex-ecuted by the physicalrobot (S to U), allowing itto recover functionalitydespite the unanticipatedchange.

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not fast enough to provide adequate feedbackduring rapid and complex motion (29). Althoughit is unlikely that organisms maintain explicit mod-els such as those presented here, the proposedmethod may shed light on the unknown processesbywhich organisms actively create and update self-models in the brain, how and which sensor-motorsignals are used to do this, what form these modelstake, and the utility of multiple competing models(30). In particular, this work suggests that directedexploration for acquisition of predictive self-models(31) may play a critical role in achieving higherlevels of machine cognition.

References and Notes1. B. Webb, Behav. Brain Sci. 24, 1033 (2001).2. R. Arkin, Behavior-Based Robotics (MIT Press, Cambridge,

MA, 1998).3. R. J. Full, D. E. Koditschek, J. Exp. Biol. 202, 3325

(1999).4. R. Pfeifer, Int. J. Cognit. Technol. 1, 125 (2002).5. T. Christaller, Artif. Life Robot. 3, 221 (1999).6. S. Nolfi, D. Floreano, Evolutionary Robotics: The Biology,

Intelligence, and Technology of Self-Organizing Machines(MIT Press, Cambridge, MA, 2000).

7. S. H. Collins, A. Ruina, R. Tedrake, M. Wisse, Science307, 1082 (2005).

8. S. Thrun, W. Burgard, D. Fox, Probabilistic Robotics (MITPress, Cambridge, MA, 2005).

9. L. Sciavicco, B. Siciliano, Modelling and Control of RobotManipulators (Springer-Verlag, London, 2001).

10. E. Alpaydin, Introduction to Machine Learning (MIT Press,Cambridge, MA, 2004).

11. K. Kozlowski, Modelling and Identification in Robotics(Springer-Verlag, London, 1998).

12. L. Ljung, System Identification: Theory for the User(Prentice-Hall, Englewood Cliffs, NJ, 1999).

13. D. Keymeulen, M. Iwata, Y. Kuniyoshi, T. Higuchi, Artif.Life 4, 359 (1998).

14. P. F. M. J. Verschure, T. Voegtlin, R. J. Douglas, Nature425, 620 (2003).

15. G. S. Hornby, S. Takamura, T. Yamamoto, M. Fujita, IEEETrans. Robot. 21, 402 (2005).

16. R. Pfeifer, C. Scheier, Understanding Intelligence (MITPress, Cambridge, MA, 1999).

17. S. H. Mahdavi, P. Bentley, Auton. Robots 20, 149 (2006).18. M. L. Visinsky, J. R. Cavallaro, I. D. Walker, Reliab. Eng.

Syst. Saf. 46, 139 (1994).19. F. Caccavale, L. Villani, P. Ax, Eds., Fault Diagnosis and

Fault Tolerance for Mechatronic Systems (SpringerVerlag, New York, 2002).

20. S. Zilberstein, R. Washington, D. S. Benstein, A.-I.Mouaddib, Lect. Notes Comput. Sci. 2466, 270 (2002).

21. H. S. Seung, M. Opper, H. Sompolinsky, in Proceedings ofthe 5th Workshop on Computational Learning Theory(ACM Press, New York, 1992), pp. 287–294.

22. J. Bongard, H. Lipson, J. Mach. Learn. Res. 6, 1651 (2005).23. J. Bongard, H. Lipson, Trans. Evol. Comput. 9, 361 (2005).24. B. Kouchmeshky, W. Aquino, J. Bongard, H. Lipson, Int. J.

Numer. Methods Eng., in press; published online 31 July2006 (doi: 10.1002/nme.1803).

25. Materials and methods are available as supportingmaterial on Science Online.

26. R. A. Brooks, in Proceedings of the 1st EuropeanConference on Artificial Life, F. J. Varela, P. Bourgine,Eds. (Springer-Verlag, Berlin, 1992), pp. 3–10.

27. R. D. King et al., Nature 427, 247 (2004).28. U. Saranli, M. Buehler, D. E. Koditschek, Int. J. Robot.

Res. 20, 616 (2001).

29. A. Maravita, C. Spence, J. Driver, Curr. Biol. 13, R531(2003).

30. G. Edelman, Neural Darwinism: The Theory of NeuronalGroup Selection (Basic Books, New York, 1987).

31. F. Crick, C. Koch, Nat. Neurosci. 6, 119 (2003).32. This research was supported in part by the NASA Program

for Research in Intelligent Systems under grantNNA04CL10A and the NSF grant number DMI 0547376.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/314/5802/1118/DC1Materials and MethodsFigs. S1 and S2ReferencesMovie S1

9 August 2006; accepted 4 October 200610.1126/science.1133687

Solid-State Thermal RectifierC. W. Chang,1,4 D. Okawa,1 A. Majumdar,2,3,4 A. Zettl1,3,4*

We demonstrated nanoscale solid-state thermal rectification. High-thermal-conductivity carbonand boron nitride nanotubes were mass-loaded externally and inhomogeneously with heavymolecules. The resulting nanoscale system yields asymmetric axial thermal conductance withgreater heat flow in the direction of decreasing mass density. The effect cannot be explained byordinary perturbative wave theories, and instead we suggest that solitons may be responsible forthe phenomenon. Considering the important role of electrical rectifiers (diodes) in electronics,thermal rectifiers have substantial implications for diverse thermal management problems,ranging from nanoscale calorimeters to microelectronic processors to macroscopic refrigeratorsand energy-saving buildings.

The invention of nonlinear solid-statedevices, such as diodes and transistors,that control electrical conduction marked

the emergence of modern electronics. It is ap-parent that counterpart devices for heat conduc-tion, if they could be fabricated, would have

Fig. 3. Distance traveled during optimized versusrandom behaviors. Dots indicate the final locationof the robot’s center of mass, when it starts at theorigin. Red dots indicate final positions of thephysical robot when executing random behaviors.Black dots indicate final expected positionspredicted by the 30 optimized behaviors whenexecuted on the self-model (Fig. 2F). Blue dotsdenote the actual final positions of the physicalrobot after executing those same behaviors inreality. The behaviors corresponding to the circleddots are depicted in Fig. 2, G to L. Squares in-dicate mean final positions. Vertical and horizon-tal lines indicate 2 SD for vertical and horizontaldisplacements, respectively.

Table 1. Performance summary for the three algorithm variants. Baseline algorithms 1 and 2disable the iterative and the model-driven nature of the learning process, respectively, whileensuring that the same computational effort and number of physical actions are used. Beforedamage, a successful experiment is determined as one that outputs a model with correct topology(see fig. S2 for examples of correct and incorrect topologies). Mean model error was calculated overthe best model from each of the 30 experiments. Mean values are reported ± SD. An additional 90experiments were conducted after the robot was damaged. The robot reinitiates modeling at thispoint using the most accurate model from the first 90 experiments (Fig. 2F). In this case, meanmodel error is determined as the difference between the inferred length of the damaged leg andthe true damaged length (9.7 cm).

Baseline 1 Baseline 2 Model-drivenalgorithm

Before damageIndependent experiments (n) 30 30 30Physical actions per experiment 16 16 16Mean model evaluations (n = 30) 262,080 ± 13,859 246,893 ± 17,469 262,024 ± 13,851Successful self-models 7 8 13Success rate 23.3% 26.7% 43.3%Mean model error (n = 30) 9.62 ± 1.47 cm 9.7 ± 1.45 cm 7.31 ± 1.22 cm

After damageIndependent experiments (n) 30 30 30Physical actions per experiment 16 16 16Mean model evaluations (n = 30) 292,430 ± 44,375 278,140 ± 37,576 296,000 ± 22,351Mean model error (n = 30) 5.60 ± 2.98 cm 4.55 ± 3.22 cm 2.17 ± 0.55 cm

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